Mathematics
Grade 11
15 min
Find the center of a circle
Find the center of a circle
What you'll learn
- Identify unit fractions (1/2, 1/3, 1/4, 1/6, 1/8) represented by shaded parts of circles and rectangles with 80% accuracy.
- Match at least 4 out of 5 given unit fractions (1/2, 1/3, 1/4, 1/6, 1/8) to their corresponding visual models (circles and rectangles).
- Explain in their own words, using the terms 'whole' and 'equal parts', why a specific shaded area represents a given unit fraction (e.g., 'This is 1/4 because one part is shaded out of four equal parts in the whole').
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Identify the center of a circle directly from its standard form equation.
Convert the general form of a circle's equation to its standard form by completing the square.
Determine the coordinates of a circle's center from its general form equation.
Calculate the center of a circle given the endpoints of its diameter using the Midpoint Formula.
Set up the necessary equations to find the center of a circle that passes through three non-collinear points.
Verify if a given point is the center of a circle defined by its equation.
Ever wondered how your phone's GPS pinpoints your location within a circular search area? 📍 It all starts with finding the center!
This tutorial will guide you through the essential methods for finding the center of a...
2
Key Concepts & Vocabulary
TermDefinitionExample
Center of a Circle (h, k)The fixed point in the interior of a circle from which all points on the circumference are equidistant.For a circle centered at the origin, the center (h, k) is (0, 0).
Standard Form of a Circle's EquationThe equation of a circle written as (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center and r is the radius.The equation (x - 2)^2 + (y + 5)^2 = 9 represents a circle with its center at (2, -5).
General Form of a Circle's EquationThe equation of a circle written as x^2 + y^2 + Dx + Ey + F = 0, where D, E, and F are constants.The equation x^2 + y^2 - 4x + 10y + 20 = 0 is in general form.
DiameterA line segment that passes through the center of a circle and has its endpoints on the circle's circumference.If a circle has its...
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Core Formulas
Center from Standard Form
Given the equation (x - h)^2 + (y - k)^2 = r^2, the center is the point (h, k).
Use this to directly identify the center when the equation is in standard form. Be careful with the signs; the coordinates are the opposite of the numbers seen in the brackets.
Midpoint Formula
For a line segment with endpoints (x_1, y_1) and (x_2, y_2), the midpoint M is M = ( (x_1 + x_2)/2 , (y_1 + y_2)/2 ).
Use this formula to find the center of a circle when you are given the coordinates of the two endpoints of a diameter.
Center from General Form
Given x^2 + y^2 + Dx + Ey + F = 0, the center (h, k) can be found using h = -D/2 and k = -E/2.
This is a shortcut derived from the process of completing the square. It allows you to find the center's coordinate...
4 more steps in this tutorial
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Challenging
A circle passes through the points A(0, 0), B(8, 0), and C(0, 6). What are the coordinates of its center?
A.(4, 3)
B.(3, 4)
C.(8, 6)
D.(0, 0)
Challenging
The center of a circle lies on the line y = x. The circle passes through the points P(1, 4) and Q(5, 2). Find the coordinates of the center.
A.(2, 2)
B.(3, 3)
C.(4, 4)
D.(2.5, 2.5)
Easy
What are the coordinates of the center of the circle with the equation (x - 5)² + (y - 2)² = 16?
A.(-5, -2)
B.(-5, 2)
C.(5, 2)
D.(5, -2)
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Frequently asked questions
What grade level is "Find the center of a circle"?
Find the center of a circle is a Grade 11 Mathematics lesson on ExcelOS.
What will I learn in Find the center of a circle?
You'll be able to: Identify unit fractions (1/2, 1/3, 1/4, 1/6, 1/8) represented by shaded parts of circles and rectangles with 80% accuracy; Match at least 4 out of 5 given unit fractions (1/2, 1/3, 1/4, 1/6, 1/8) to their corresponding visual….
Is "Find the center of a circle" free to practice?
Yes. You can read the tutorial preview for free, and signing up for a free ExcelOS account unlocks the full tutorial and all practice questions with instant feedback.
How many practice questions are included with Find the center of a circle?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.